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We first show the existence of an effective determinantal representation forany univariate polynomial with real coefficients. Then, we more preciselyestablish that any univariate polynomial with real coefficients has aneffective determinantal representation with signature (r+s,s) if and only if ithas at least r real roots with multiplicity. The effective determinantalrepresentations we construct used arrow matrices.

Repr\'esentations d\'eterminantales effectives des polyn\^omes univari\'es par les matrices fl\`eches